I noticed in the opening address at the October 2012 General Conference, that -- at least in the context of a speech -- the terms "sin" and "transgression" were stressed independently and each more than once.

The terminology used by the LDS church is often recognizably similar to that of other groups, but the exactly meanings given them is often different.

Is this just a a repetition to highlight the importance of the issue or do the terms have different shades of meanings according to LDS doctrine?

This suggested contrast between a sin and a transgression reminds us of the careful wording in the second article of faith: “We believe that men will be punished for their own sins, and not for Adam’s transgression”. It also echoes a familiar distinction in the law. Some acts, like murder, are crimes because they are inherently wrong. Other acts, like operating without a license, are crimes only because they are legally prohibited. Under these distinctions, the act that produced the Fall was not a sin—inherently wrong—but a transgression—wrong because it was formally prohibited. These words are not always used to denote something different, but this distinction seems meaningful in the circumstances of the Fall.

Further, It has been said that Adam and Eve merely transgressed the law because they did not yet know the difference between good and evil, and thus they were not accountable for sin. A similar argument is used to say that children cannot sin; they are not accountable. They do, however, trangress laws.

The distinction between the two terms is not always clear cut though and invariably the two will be used interchangeably despite the subtle difference.

The two terms are often used interchangeably, in line with John's declaration that "sin is the transgression of the law." (1 John 3:4) However, there is at least one significant point in LDS doctrine where the two terms are treated as distinct.

We believe that men will be punished for their own sins, and not for Adam’s transgression.

LDS theology does not recognize the concept of "Original Sin" as it is generally understood in other Christian denominations, the idea that the Fall causes all mankind to be inherently sinful and inherit guilt and condemnation from Adam's actions. The Fall of Adam is understood to be a transgression of God's law, but not an inherently sinful act, as it was a part of God's plan: in order for God's children to progress, they had to live in an imperfect environment where they would be subject to temptation, that they could learn the difference between good and evil for themselves, and learn to live by faith, and choose good and reject evil.

One of the implications of this doctrine is that, as all men are accountable only for their own personal sins, and not for the acts of Adam or anyone else, this means that children are born in a state of innocence and do not require baptism for the removal of the guilt of Original Sin. Moroni chapter 8 from the Book of Mormon lays out this doctrine in clear (and fairly strong) words.